which equals the standard low-energy effective potential for the minimum value
\(U=\hbar ^2/4\)  [1]}, [2]}. For the harmonic oscillator, for instance,
\(V^{\prime \prime }(q)=m\omega ^2\)  implies the correct zero-point energy
\(\frac{1}{2}\hbar \omega \) . A higher-order adiabatic approximation implies
higher-derivative corrections to the classical equations of motion
[3]}. An adiabatic approximation to all orders would imply a
non-local theory with time derivatives of arbitrarily high orders, which can
more easily be studied by keeping \(s\)  as an independent field in a
non-adiabatic formulation.
